Find the prime factorization of number 32768.

Answer

The prime factorization of 32768 is:

$$ 32768 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2 $$

Which is the same as :

$$ 32768 = 2^{15} $$

Prime factorization can be nicely visualized by creating a factorization tree.

32768 can be written as 2 × 16384.	32768 2 16384
16384 can be written as 2 × 8192.	32768 2 16384 8192 2
8192 can be written as 2 × 4096.	32768 2 16384 8192 2 4096 2
4096 can be written as 2 × 2048.	32768 2 16384 8192 2 4096 2048 2 2
2048 can be written as 2 × 1024.	32768 2 16384 8192 2 4096 2048 2 1024 2 2
1024 can be written as 2 × 512.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 2 2
512 can be written as 2 × 256.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 2 2 2
256 can be written as 2 × 128.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 2 2 2
128 can be written as 2 × 64.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 2 2 2 2
64 can be written as 2 × 32.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 2 2 2 2
32 can be written as 2 × 16.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 2 2 2 2 2
16 can be written as 2 × 8.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 2 2 2 2 2
8 can be written as 2 × 4.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2
4 can be written as 2 × 2.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2 2 2
The end nodes are the prime factors of the number 32768.	32768 2 16384 8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2 2 2

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